exim & mail queue problem

A few of my clients are complaining because they're not receiving their emails. I have noticed
that their mails remain in the mail queue until i press "Deliver now", only then they receive their emails.
Any solutions?

as i said...i don't like giving the root password to anybody,not even cpanel

the ouput of those commands was 0...i mean there were no emails in the mail queue(for now), not frozen, nothing!

Spam is out of disscussion.I have checked, i'm 100% there was no spam.
Do you think it is possible that it happened because the size of the emails was too large?
I've noticed that there were a few emails were a few MBs...

You should check the exim logs to see why the email remain in queue. Before click on "Deliver now", copy the message ID and search for it in logs:

exigrep YOUR-MESSAGE-ID /var/log/exim_mainlog

In this way, you will find when the message was received by server and why doesn't work the first attempt to deliver it. Usually this happens when there are too many mails in queue or if the recipient is reading the email (I think only in mailbox but new versions of cPanel use maildir)